Optimal. Leaf size=24 \[ -\frac {2 b x^{n-1} \sqrt {b x^n}}{2-3 n} \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac {2 b x^{n-1} \sqrt {b x^n}}{2-3 n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^n\right )^{3/2}}{x^2} \, dx &=\left (b x^{-n/2} \sqrt {b x^n}\right ) \int x^{-2+\frac {3 n}{2}} \, dx\\ &=-\frac {2 b x^{-1+n} \sqrt {b x^n}}{2-3 n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.92 \[ \frac {\left (b x^n\right )^{3/2}}{\left (\frac {3 n}{2}-1\right ) x} \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x^{n}\right )^{\frac {3}{2}}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.83 \[ \frac {2 \left (b \,x^{n}\right )^{\frac {3}{2}}}{\left (3 n -2\right ) x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 22, normalized size = 0.92 \[ \frac {2\,b\,x^{n-1}\,\sqrt {b\,x^n}}{3\,n-2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \begin {cases} \frac {2 b^{\frac {3}{2}} \left (x^{n}\right )^{\frac {3}{2}}}{3 n x - 2 x} & \text {for}\: n \neq \frac {2}{3} \\\int \frac {\left (b x^{\frac {2}{3}}\right )^{\frac {3}{2}}}{x^{2}}\, dx & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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